Monotone $\alpha$-nonexpansive mapping in ordered Banach space by AU-iteration algorithm with application to delay differential equation

Document Type : Review articles

Authors

Department of Mathematics, Michael Okpara University of Agriculture, Umudike, Abia State, Nigeria

Abstract

In this paper, we adopt the AU-iteration scheme introduced by Udofia et. al. [21] (U. E. Udofia, A. E. Ofem, and D. I. Igbokwe, Convergence Analysis for a New Faster Four Steps Iterative Algorithm with an Application, Open J. Math. Anal., 5  (2021), no. 2, 95--112) to approximate the fixed point of monotone $\alpha$-nonexpansive mappings in ordered Banach space. Analytically and with a numerical example we show that this iteration process converges faster than some well known existing iteration processes in literature. Further, we apply the AU-iteration process to find the unique solutions of a delay differential equation.

Keywords

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Volume 13, Issue 2
July 2022
Pages 673-690
  • Receive Date: 02 March 2021
  • Revise Date: 16 March 2022
  • Accept Date: 10 April 2022